Question

1. a restaurant chain advertises that its ice - cream sundaes weigh 8.3 oz., but a customer suspects they weigh less.

a. state appropriate null and alternative hypotheses in words.

• $h_0$: the mean weight of all ice - cream sundaes is 8.3 oz. vs. $h_a$: the mean weight of all ice - cream sundaes is not 8.3 oz.
• $h_0$: the mean weight of all ice - cream sundaes is 8.3 oz. vs. $h_a$: the mean weight of all ice - cream sundaes is 8.3 oz.
• $h_0$: the mean weight of all ice - cream sundaes is not 8.3 oz. vs. $h_a$: the mean weight of all ice - cream sundaes is 8.3 oz.
• $h_0$: the mean weight of all ice - cream sundaes is 8.3 oz. vs. $h_a$: the mean weight of all ice - cream sundaes is less than 8.3 oz.

b. state appropriate null and alternative hypotheses in symbols.

• $h_0:mu = 8.3$ vs. $h_a:mu<8.3$
• $h_0:mu<8.3$ vs. $h_a:mu = 8.3$
• $h_0:mu = 8.3$ vs. $h_a:mu>8.3$
• $h_0:mu = 8.3$ vs. $h_a:mu

eq8.3$

1. stacy claims she can long - jump 20 ft. on average. you observe a random sample of jump distances, and other evidence suggests she can jump on average of 20 ft or less.

a. state appropriate null and alternative hypotheses in words.

• $h_0$: the mean jump distance is less than 20 ft. vs. $h_a$: the mean jump distance is 20 ft.
• $h_0$: the mean jump distance is 20 ft. vs. $h_a$: the mean jump distance is less than 20 ft.
• $h_0$: the mean jump distance is 20 ft. vs. $h_a$: the mean jump distance is not 20 ft.
• $h_0$: the mean jump distance is not 20 ft. vs. $h_a$: the mean jump distance is 20 ft.

b. state appropriate null and alternative hypotheses in symbols.

• $h_0:mu = 20$ vs. $h_a:mu

eq20$

• $h_0:mu

eq20$ vs. $h_a:mu = 20$

• $h_0:mu = 20$ vs. $h_a:mu>20$
• $h_0:mu<20$ vs. $h_a:mu = 20$

1. wildlife managers have long monitored the shell thickness of a particular kind of prey as an index of the health of the population. during the last several years, the mean thickness was 0.6 mm (assume $mu_0$ is the mean thickness of the entire population of eggshells for this species). a researcher suspects the eggshell thickness has changed.

a. state appropriate null and alternative hypotheses in words.

• $h_0$: the mean eggshell thickness is less than 0.6 mm. vs. $h_a$: the mean eggshell thickness is 0.6 mm.
• $h_0$: the mean eggshell thickness is 0.6 mm. vs. $h_a$: the mean eggshell thickness is not 0.6 mm.
• $h_0$: the mean eggshell thickness is 0.6 mm. vs. $h_a$: the mean eggshell thickness is less than 0.6 mm.
• $h_0$: the mean eggshell thickness is not 0.6 mm. vs. $h_a$: the mean eggshell thickness is 0.6 mm.

b. state appropriate null and alternative hypotheses in symbols.

• $h_0:mu = 0.6$ vs. $h_a:mu

eq0.6$

• $h_0:mu

eq0.6$ vs. $h_a:mu = 0.6$

• $h_0:mu = 0.6$ vs. $h_a:mu>0.6$
• $h_0:mu = 0.6$ vs. $h_a:mu<0.6$

Explanation:

1.

• a. For the ice - cream sundae weight problem:
• The null hypothesis \(H_0\) is usually a statement of no effect or equality. The alternative hypothesis \(H_a\) is what we suspect to be true instead. If the manufacturer claims the mean weight is \(8.3\) oz and the customer suspects they weigh less, the correct pair of hypotheses is:
• \(H_0:\mu = 8.3\) vs \(H_a:\mu<8.3\)
• Answer: The correct option is the one with \(H_0:\mu = 8.3\) vs \(H_a:\mu < 8.3\) (not explicitly numbered in the question - but this is the correct pair).
• b. In symbolic form:
• The null hypothesis \(H_0\) is the statement of equality, and the alternative \(H_a\) is the statement of the suspected non - equality. So \(H_0:\mu = 8.3\) vs \(H_a:\mu<8.3\)

2.

• a. For the long - jump distance problem:
• If the claim is that she can jump \(20\) ft on average and we want to test if there is evidence to support this or not, the null hypothesis \(H_0\) is the statement of the claim (equality) and the alternative \(H_a\) is the non - equality statement. So \(H_0:\mu = 20\) vs \(H_a:\mu

eq20\)

• Answer: The correct option is the one with \(H_0:\mu = 20\) vs \(H_a:\mu

eq20\) (not explicitly numbered in the question - but this is the correct pair).

• b. In symbolic form:
• \(H_0:\mu = 20\) vs \(H_a:\mu

eq20\)
3.

• a. For the eggshell thickness problem:
• If the long - established average thickness is \(0.6\) mm and we want to test if it has changed, the null hypothesis \(H_0\) is the statement of equality (no change) and the alternative \(H_a\) is the non - equality statement. So \(H_0:\mu = 0.6\) vs \(H_a:\mu

eq0.6\)

• Answer: The correct option is the one with \(H_0:\mu = 0.6\) vs \(H_a:\mu

eq0.6\) (not explicitly numbered in the question - but this is the correct pair).

• b. In symbolic form:
• \(H_0:\mu = 0.6\) vs \(H_a:\mu

eq0.6\)

Answer:

1.

• a. For the ice - cream sundae weight problem:
• The null hypothesis \(H_0\) is usually a statement of no effect or equality. The alternative hypothesis \(H_a\) is what we suspect to be true instead. If the manufacturer claims the mean weight is \(8.3\) oz and the customer suspects they weigh less, the correct pair of hypotheses is:
• \(H_0:\mu = 8.3\) vs \(H_a:\mu<8.3\)
• Answer: The correct option is the one with \(H_0:\mu = 8.3\) vs \(H_a:\mu < 8.3\) (not explicitly numbered in the question - but this is the correct pair).
• b. In symbolic form:
• The null hypothesis \(H_0\) is the statement of equality, and the alternative \(H_a\) is the statement of the suspected non - equality. So \(H_0:\mu = 8.3\) vs \(H_a:\mu<8.3\)

2.

• a. For the long - jump distance problem:
• If the claim is that she can jump \(20\) ft on average and we want to test if there is evidence to support this or not, the null hypothesis \(H_0\) is the statement of the claim (equality) and the alternative \(H_a\) is the non - equality statement. So \(H_0:\mu = 20\) vs \(H_a:\mu

eq20\)

• Answer: The correct option is the one with \(H_0:\mu = 20\) vs \(H_a:\mu

eq20\) (not explicitly numbered in the question - but this is the correct pair).

• b. In symbolic form:
• \(H_0:\mu = 20\) vs \(H_a:\mu

eq20\)
3.

• a. For the eggshell thickness problem:
• If the long - established average thickness is \(0.6\) mm and we want to test if it has changed, the null hypothesis \(H_0\) is the statement of equality (no change) and the alternative \(H_a\) is the non - equality statement. So \(H_0:\mu = 0.6\) vs \(H_a:\mu

eq0.6\)

• Answer: The correct option is the one with \(H_0:\mu = 0.6\) vs \(H_a:\mu

eq0.6\) (not explicitly numbered in the question - but this is the correct pair).

• b. In symbolic form:
• \(H_0:\mu = 0.6\) vs \(H_a:\mu

eq0.6\)